Knowledge Dependency and Update for Knowledge-Bases Using DOT Notation and IS-A Relation

Abstract

We have developed a knowledge representation scheme DOT based on the dot notation and the IS-A relations between objects, and demonstrated that DOT gives a simple mathematical foundation for expressing the inheritance relationship between objects in deductive and object-oriented databases. As an extended research on the DOT scheme, we define in this paper the dependency of knowledge as a logical formula that expresses a specific IS-A relationship of DOT from which the knowledge is deduced in knowledge-bases. Then we propose a framework of knowledge based on the DOT in which negative knowledge is manipulated under the relationship to the notion of consistency constraint in database systems. Finally, employing developed dependency formulae, we propose an efficient update processing method which requires a small number of knowledge-base access and reduces the redundancy in closure calculation.